Approximation of the Willmore energy by a discrete geometry model-Reference-Cited by-同舟云学术

Approximation of the Willmore energy by a discrete geometry model

Published:2021-08-25 Issue:0 Volume:0 Page:
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Gladbach Peter¹,Olbermann Heiner²

Affiliation:

1. Institut für Angewandte Mathematik , Universität Bonn , 53115 Bonn , Germany

2. Institut de Recherche en Mathématique et Physique , UCLouvain , 1348 Louvain-la-Neuve , Belgium

Abstract

Abstract We prove that a certain discrete energy for triangulated surfaces, defined in the spirit of discrete differential geometry, converges to the Willmore energy in the sense of Γ-convergence. Variants of this discrete energy have been discussed before in the computer graphics literature.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2020-0094/pdf

Reference30 articles.

1. R. Alicandro, A. Braides and M. Cicalese, Continuum limits of discrete thin films with superlinear growth densities, Calc. Var. Partial Differential Equations 33 (2008), no. 3, 267–297.

2. R. Alicandro and M. Cicalese, A general integral representation result for continuum limits of discrete energies with superlinear growth, SIAM J. Math. Anal. 36 (2004), no. 1, 1–37.

3. R. Alicandro and M. Cicalese, Variational analysis of the asymptotics of the X⁢YXY model, Arch. Ration. Mech. Anal. 192 (2009), no. 3, 501–536.

4. R. Alicandro, M. Cicalese and A. Gloria, Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity, Arch. Ration. Mech. Anal. 200 (2011), no. 3, 881–943.

5. R. Alicandro, L. De Luca, A. Garroni and M. Ponsiglione, Metastability and dynamics of discrete topological singularities in two dimensions: A Γ-convergence approach, Arch. Ration. Mech. Anal. 214 (2014), no. 1, 269–330.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Modeling self-aggregation of stochastic particles: A Γ-convergence approach;Mathematical Models and Methods in Applied Sciences;2024-07-27